Problem: Solve for $x$ and $y$ using elimination. ${-5x+3y = -47}$ ${3x-3y = 27}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-2x = -20$ $\dfrac{-2x}{{-2}} = \dfrac{-20}{{-2}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-5x+3y = -47}\thinspace$ to find $y$ ${-5}{(10)}{ + 3y = -47}$ $-50+3y = -47$ $-50{+50} + 3y = -47{+50}$ $3y = 3$ $\dfrac{3y}{{3}} = \dfrac{3}{{3}}$ ${y = 1}$ You can also plug ${x = 10}$ into $\thinspace {3x-3y = 27}\thinspace$ and get the same answer for $y$ : ${3}{(10)}{ - 3y = 27}$ ${y = 1}$